Lévy area for Gaussian processes: A double Wiener-ItÔ integral approach

Albert Ferreiro-Castilla, Frederic Utzet

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1 Citation (Scopus)

Abstract

Let (X1(t))0≤t≤1 and (X2(t))0≤t≤1 be two independent continuous centered Gaussian processes with covariance functions R1 and R2. We show that if the covariance functions are of finite p-variation and q-variation respectively and such that p-1+q-1>1, then the Lévy area can be defined as a double Wiener-ItÔ integral with respect to an isonormal Gaussian process induced by X1 and X2. Moreover, some properties of the characteristic function of that generalised Lévy area are studied. © 2011 Elsevier B.V.
Original languageEnglish
Pages (from-to)1380-1391
JournalStatistics and Probability Letters
Volume81
Issue number9
DOIs
Publication statusPublished - 1 Sep 2011

Keywords

  • 60G15
  • 60G22
  • 60H05
  • Fractional Brownian motion
  • Lévy area
  • Multiple Wiener-ItÔ integral
  • P-variation
  • Young's inequality

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